Just to pull back some of the links from up thread.
You can also check the video @Grey_Devil linked where Witty discusses a lot of the context around how BBQ worked.
This claim, and claims like it come out of a lot of misunderstanding about how food worked in the past. And are mostly drawn from just so stories about Southern food that portray everything as derived from happy slaves or the results of Gone With the Wind fictional Antebellum culture.
Meat was not handled this way at the time, outside of cities and especially meat packing areas animals were not cut into individual cuts and distributed. Particularly in the hot South, meat either needed to be cured and smoked to preserve it, or cooked day of. And fresh meat was not available year round. Barbeque was an occasional, community activity. Where whole animals would be killed during harvest/slaughter parts of the year. And cooked whole. For special occasions like church events, weddings, or especially political campaign events whole animals would be slaughtered off season specifically for BBQ.
This was not home cooking, it was a once or twice a year sort of thing. And counter to what’s portrayed by the typical stories of Southern food. Slaves did not generally have the run of things to have happy hoedowns of their own volition, or share in the supplies of the the main house. There was a separate provision system just to provide for them. There were vastly more slaves on a plantation then there were owners and white staff. And if hogs were being raise they were being raised for sale. Where slaves were given fresh meat at all it was almost always chicken, even that was a rarity. Even tough and boney cuts when fresh were a desirable rarity, they wouldn’t be passed to slaves. They’d be eaten by the white folks.
To slaughter animals off season, or afford to buy them you’re typically talking about fairly well off people or people with good size herds. Which means slave owners. So the animals for these big community events were most often provided in some fashion by slave owners, wealthier folks, prominent people (quite often politicians!).
And that points to the real connection here. Those people also provided the service of cooking the Barbeque. And as a result the vast majority of pitmasters were black slaves, as were the servents who served it all and handled everything else.
So enslaved blacks were used to cook barbeque, for white celebrations. And this was infact a business. With owners who had talented slave cooks, selling their services (and the meat) for large scale barbeque events. Just like modern catering.